Lithium Battery???

Those batteries are tiny, they're what I use when I do lighting modifications,



Firstly you would have trouble mounting one in the battery compartment, secondly they don't have enough power, I imagine it wouldn't have enough to turn the motor, but even if it did, it would be flat in less than a minute!

With batteries you have x2 things to consider, the voltage & the capacity, my AA rechargeable batteries are around 2000mah

If you want to get a better battery your really limited to the common sizes (if your wanting a disposable type) other wise there are a lot of Radio Control type batteries which would be suitable, as these are more specialised you would have to do some research on physical sizings to ensure they fit, secondly the best batteries are lipo types (like used in radio controlled helicopters) they are really good but have limiting constraints for example, if you over discharge them they become damaged. So you need suitable protection circuits (you can buy these) but you will also need a suitable charger. if your serious about it the battery type you need to look at us 3.7v 1s lipo cell, they generally look like this,




Then the voltage alarm, it needs to be suitable for the battery, if you use a 1s type like above you need a compatible battery alarm, this will alarm (usually audibly) when the battery needs recharging,



This will need to fit under the trains body shell to, or at least in the tender or first carriage,

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Edit, I just re read your post the cr123A is different to what I thought, it looks like it should work although it doesn't look like a direct replacement for AA or C,